53 citations · 163 across the 21 of their papers we have counts for
24 papers
Cohomologically tropical varieties
Edvard Aksnes, Omid Amini, Matthieu Piquerez +1
Given the tropicalization of a complex subvariety of the torus, we define a morphism between the tropical cohomology and the rational cohomology of their respective tropical compac…
Avoidance loci and tropicalizations of real bitangents to plane quartics
Hannah Markwig, Sam Payne, Kris Shaw
We compare two partitions of real bitangents to smooth plane quartics into sets of 4: one coming from the closures of connected components of the avoidance locus and another coming…
On the birational geometry of matroids
Kris Shaw, Annette Werner
This paper investigates isomorphisms of Bergman fans of matroids respecting different fan structures, which we regard as matroid analogs of birational maps. We show that isomorphis…
Real phase structures on matroid fans and matroid orientations
Johannes Rau, Arthur Renaudineau, Kris Shaw
We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over $\mathbb{Z}/2\mathb…
Tropical floor plans and enumeration of complex and real multi-nodal surfaces
Hannah Markwig, Thomas Markwig, Kristin Shaw +1
The family of complex projective surfaces in projective three space of degree having precisely nodes as their only singularities has codimension in the linear system of…
Toric degenerations of Grassmannians from matching fields
Fatemeh Mohammadi, Kristin Shaw
We study the algebraic combinatorics of monomial degenerations of Plücker forms which is governed by matching fields in the sense of Sturmfels and Zelevinsky. We provide a necessar…